Symmetry fractionalization and duality defects in Maxwell theory
Naoto Kan (Department of Physics, Osaka University, Machikaneyama-Cho 1-1, Toyonaka, 560-0043, Japan); Kohki Kawabata (Department of Physics, Faculty of Science, The University of Tokyo, Bunkyo-Ku, Tokyo, 113-0033, Japan); Hiroki Wada (Department of Physics, Osaka University, Machikaneyama-Cho 1-1, Toyonaka, 560-0043, Japan)
We consider Maxwell theory on a non-spin manifold. Depending on the choice of statistics for line operators, there are three non-anomalous theories and one anomalous theory with different symmetry fractionalizations. We establish the gauging maps that connect the non-anomalous theories by coupling them to a discrete gauge theory. We also construct topological interfaces associated with SL(2, ℤ) duality and gauging of electric and magnetic one-form symmetries. Finally, by stacking the topological interfaces, we compose various kinds of duality defects, which lead to non-invertible symmetries of non-spin Maxwell theories.
